Abstract
In recent years the Maximum Entropy Principle has been used to develop radically new approaches to various classes of optimization problems such as those of scalar non-linear constrained optimization, vector and minimax optimization. In this paper two new entropy-based approaches are developed, proved and applied to the problem of generating Pareto optimal solution sets for general multi-criteria optimization problems. The solution algorithms are applied to several test problems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Cohon, J.L., Multi Objective Programming and Planning, New York: Academic Press, 1978.
Gere, J.S., Optimization in Computer Aided Design, New York: North-Holand, 1983.
Hardy, G.H., Littlewood, J.E. and Palya, G., Inequalities, Cambridge: Cambridge University Press, 1934.
Jaynes, E.T., ‘Information Theory and Statistical Mechanics’, The Physical Review, Vol. 106, pp. 620–630 and Vol. 108, pp. 171–190, 1957.
Li, X.S., ‘Entropy and Optimization’, Ph.D. Thesis, Liverpool: Liverpool University, 1987.
Marglin, S., Public Investment Criteria, Cambridge, Mass.: MIT Press, 1967.
Osyczka, A., Multicriterion Optimization in Engineering, Chichester: Ellis Horwood, 1984.
Shannon, C.E., ‘A Mathematical Theory of Communication’, Bell System Technical Journal, Vol. 27, No. 3, pp. 379–428, 1948.
Singh, N. and Dutta, S.P., ‘Some Multi-Objective Approaches to Diamond Dressing Optimization’, J. of Eng. Optimization, Vol. 12, pp. 235–245, 1987.
Steuer, R.E., Multiple Criteria Optimization: Theory, Computation and Application, J. Wiley, 1986.
Sultan, A.M., ‘Entropic Vector Optimization and Simulated Entropy: Theory & Applications’, Ph.D. Thesis, Liverpool: Liverpool University, 1990.
Templeman, A.B. and Li, X.S., ‘A maximum entropy approach to constrained nonlinear programming’, Eng. Optimization, Vol. 12, No. 2, pp. 191–205, 1987.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Sultan, A.M., Templeman, A.B. (1996). Generation of Pareto Solutions by Entropy-Based Methods. In: Tamiz, M. (eds) Multi-Objective Programming and Goal Programming. Lecture Notes in Economics and Mathematical Systems, vol 432. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-87561-8_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-87561-8_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60662-8
Online ISBN: 978-3-642-87561-8
eBook Packages: Springer Book Archive